Does 1 over square root 2 equal square root 1/2?

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Does 1 over square root 2 equal square root 1/2?

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Answer 1 · 2015-05-30T14:46:30

Yep.
You have:
$\frac{a}{\sqrt{2}} =$ $a/sqrt(2)=$ you can take the root of the numerator (which in this case is $a = 1$ $a=1$ ) but you have always to square it (to avoid changing your fraction) so you get:
$\frac{\sqrt{a^{2}}}{\sqrt{2}}$ $sqrt(a^2)/sqrt(2)$ you can use one square root only:
$= \sqrt{\frac{a^{2}}{2}} =$ $=sqrt(a^2/2)=$ but in this case $a = 1$ $a=1$ so that $1^{2} = 1$ $1^2=1$ so you get $= \sqrt{\frac{1}{2}}$ $=sqrt(1/2)$

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Does 1 over square root 2 equal square root 1/2?

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